Statistica Sinica 19 (2009), 363-375

CHARACTERIZATION OF GENERAL MINIMUM LOWER

ORDER CONFOUNDING VIA COMPLEMENTARY SETS

Runchu Zhang$^{1,2}$ and Rahul Mukerjee$^3$

$^1$Northeast Normal University, $^2$Nankai University

and $^3$Indian Institute of Management Calcutta

Abstract: With reference to regular fractions of general $s$-level factorials, we consider the design criterion of general minimum lower order confounding (GMC) that aims, in an elaborate manner, at keeping the lower order factorial effects unaliased with one another to the extent possible. Using a finite projective geometric formulation, this involves identification of the alias sets with the points of the geometry; we derive explicit formulae connecting the key terms for this criterion with the complementary set. These results are then applied to find optimal designs under the GMC criterion.

Key words and phrases: Alias set, effect hierarchy principle, finite projective geometry, minimum aberration.